Translation Ovoids of Generalized Quadrangles and Hexagnos |
| |
Authors: | I. Bloemen J. A. Thas H. Van Maldeghem |
| |
Affiliation: | (1) Department of Pure Mathematics and Computer Algebra, University Ghent, Galglaan 2, 9000 Gent, Belgium |
| |
Abstract: | We define the notion of a translation ovoid in the classical generalized quadrangles and hexagons of order q, and we enumerate all known examples; translation spreads are defined dually. A modification of the known ovoids in the generalized hexagon H(q), q=32h+1, yields new ovoids of that hexagon. Dualizing and projecting along reguli, we obtain an alternative construction of the Roman ovoids due to Thas and Payne. Also, we construct a new translation spread in H(q) for any 1 mod 3, q odd, with the property that any projection along reguli yields the classical ovoid in the generalized quadrangle Q(4,q). Finally, we prove that for q odd, the new example is the only non-Hermitian translation spread in H(q) with the property that any projection along reguli yields the classical ovoid in Q(4,q). |
| |
Keywords: | ovoids spreads classical generalized polygons. |
本文献已被 SpringerLink 等数据库收录! |
|